Solving Systems of Equations: Word Problems
This worksheet focuses on solving real-world problems using systems of linear equations for 6th-grade students.
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Solving Systems of Equations: Word Problems
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Read each word problem carefully. Set up a system of two linear equations with two variables, then solve for the unknown values. Show all your work.
1. The sum of two numbers is 30. Their difference is 10. What are the two numbers?
2. A farmer has chickens and pigs. He counts 20 heads and 56 legs. How many chickens and how many pigs does he have?
3. The perimeter of a rectangle is 40 cm. The length is 4 cm more than the width. Find the length and width of the rectangle.
4. Sarah bought 5 apples and 3 bananas for $6.50. Mark bought 2 apples and 4 bananas for $5.00. How much does one apple cost and how much does one banana cost?
5. A movie theater sells adult tickets for $12 and child tickets for $8. If they sold a total of 300 tickets for a revenue of $3200, which system of equations represents this situation?
x + y = 300 12x + 8y = 3200
x + y = 3200 12x + 8y = 300
12x + y = 300 x + 8y = 3200
8x + 12y = 300 x + y = 3200
6. Use the system of equations from the previous problem (Question 5) to find out how many adult tickets and child tickets were sold.